Here's a secret: everything that makes "regular" printers work is vendor specific software that came pre-installed with Windows 7. Printers that did not have their drivers preinstalled, either because they are rare, old, or released after the time when Windows 7 bundled their software. It's barely different or better to have to install some driver versus use the included driver. In fact, an installed driver will likely be more up to date.
Here's another secret: Your computer can talk to any network printer regardless of wether that printer is networked in a wireless or wired fashion. This is similar to the idea that your computer can one day talk to both wired and wireless usb devices, when they become common place. Either way, your operating system needs a driver to help it decide how to send it print jobs and to know what features (double-sided, page sizes, trays, color or grayscale) it supports. Had all printers been PostScript or it's derivatives this would have been less of an issue, but that wasn't to be.
Certain parts of the software you are talking about for your printer are not the driver itself. These tools help to configure and setup the printer on your network. These only need to be run once and generally do not need to be installed on multiple machines. Another tip is that most HP Printers have good zeroconf/Bonjour support, and installing Apple's Bonjour for Windows might get you a better setup experience than trying to wrangle with Window's device discovery and printer adding system.